david.williams

-> Wow, from this it looks like it's going to be orbitting at the L2
-> Lagrangian Point, which would mean that it is stationary with respect to
-> the Earth and the Sun, and it will be behind the Earth on the night side
-> of the planet at all times, 1.5 million km's out. If it's behind the
-> Earth, wouldn't it automatically be shielded from the Sun's rays? Or is
-> the Earth's shadow not big enough out there?

The umbra of the moon's shadow *just* reaches the earth, which is
380,000 km away. The earth's diameter is four times the moon's, so the
umbra of its shadow should reach 4 x 3.8e5 km, which is very close to
the 1.5 million that you mentioned. So, if our figures are correct, the
spacecraft *might just* be shielded from sunlight, but it would have to
be very accurately positioned.

dow

david.williams

-> Actually, the webpage I linked to showed that it's got solar panels, and
-> in fact it's got something that no other space craft has ever had, a
-> huge sunshade which protects the telescope from the Sun. So obviously,
-> NASA thinks the Sun is still going to be visible from the L2 point. I
-> was just wondering out loud how big the Earth's shadow could be at that
-> distance?

-> Yousuf Khan

There are two parts to a shadow - the umbra, where the sun is totally
hidden, and the penumbra where it is partly hidden. Obviously, if the
viewpoint is so far from the earth that earth appears smaller than the
sun, then earth cannot totally hide the sun, so there is no umbra of
the earth's shadow at that distance. But there is a penumbra, which
theoretically stretches out to an infinite distance.

As seen from the neighbourhood of earth, the angular diameter of the
sun is about half a degree, or 1/117 radian. So the earth will appear
with the same angular diameter if seen from a distance of 117 times the
diameter of the earth. So that comes to 117 x 13,000 km, which is just
slightly more than 1.5 million km. So a spacecraft that's 1.5 million
km out could *just* see the sun totally covered by earth, but it would
have to be exactly positioned in the very small diameter of the umbra
of the shadow. If the distance of the spacecraft from earth is 99% of
the length of the umbra, then the diameter of the umbra will be only 1%
of the diameter of the earth, i.e. 130 kilometres, so the spacecraft
will have to keep within that small diameter.

Of course, refraction in earth's atmosphere will allow some sunlight to
reach the spacecraft even within the umbra.

dow